Sample Size Calculation for Comparing Proportions

In clinical research, in addition to continuous responses, primary clinical endpoints for assessment of efficacy and safety of a drug product under investigation could be binary responses. For example, in cancer trials, patients’ clinical reaction to the treatment is often classified as response (e.g., complete response or partial response) or nonresponse. Based on these binary responses, the proportions of the responses between treatment groups are then compared to determine whether a statistical/clinical difference exists. Appropriate sample size is usually calculated based on a statistical test used to ensure that a desired power exists for detecting such a difference when the difference truly exists. Statistical test procedures employed for testing the treatment effect with binary response are various chi-square or Z-type statistics, which may require a relatively large sample size for the validity of the asymptotic approximations. This article will focus on sample size calculation for binary responses based on asymptotic approximations. In practice, the objective of sample size calculation is to select the minimum sample size in such a way that the desired power can be obtained for detection of a clinically meaningful difference at the prespecified significance level. Therefore, the selection of the sample size depends on the magnitude of the clinically meaningful difference, the desired power, the prespecified significance level, and the hypotheses of interest under the study of